The multi-year deal is believed to be worth $100m (£82 million), according to the Wall Street Journal.
Rogan's podcast, which is one of the most popular in the world, will arrive on the streaming giant on 1 September.
It will then be housed there exclusively by the end of the year, and removed from all other platforms.
"They want me to just continue doing it the way I'm doing it right now.
"I'm excited to have the support of the largest audio platform in the world and I hope you folks are there when we make the switch!"